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Plus a few of those chemical hand warmer shake-em-up things

I took a dunking one year, my first and hopefully my last ;D
I was wearing rain gear and over my nylon pants and shirt, with a fleece vest. I got to shore, removed the fleece vest, wrung and whirled it semi-dry, and put my raincoat back on. I opened a few of those chemical heater packs and placed one over my kidney area, tucked into my waistband to hold them. I pulled my hands into my armpit area settled into comfortable spot behind a big boulder for a windbreak, and tucked into a ball. Within minutes my core temp was up, and I had to open my pit zipper vents and pull my hood back.

My gear was dry, so I just resumed paddling. If I had to build a fire, dry gear or stay where I was at, the chemical packs would of made the job much easier. Cold numb fingers and falling body temp are a bad combination.

Another variation on your fish " stick" method is a little quicker but would require more care on the dining end.

Gut your fish, leaving head on. Take 2 green sticks just big enough to hold weight of fish. Sharpen one end of each, and starting at tail, thread first from outside, thru ribs, up so far then out again, then thru gills and out the mouth. You can leave the sticks alone, or tie ground ends together with a couple short pieces of cord. Grill as you described.

An alternative IF you don't have the necessary knife/skill or patience to prepare as you described.
I have a outdoor skills book, that shows the Native people using a single spear like stick, stuck thru the gills crossway's of a NP that has just been gutted. They suspended the pike over coals and used a couple of green sticks crosswise to keep the body cavity open. Roasted/smoked until a sharp knife/stick would push thru easily from the skin side.